A rectangular container, 90 cm by 45 cm by 50 cm, is filled with water to a height of 11 cm. The ratio of the volume of water in the container to that in a bucket is 11 : 6. If ³₅ of the bucket is filled with water, find

1. the volume of the bucket.
2. the minimum number of such buckets to fill the container.

(a)
Volume of water in the container
= 90 x 45 x 11
= 44550 cm³ 

11 u = 44550 cm³ 
1 u = 44550 ÷ 11 = 4050 cm³ 
6 u = 6 x 4050 = 24300 cm³ 

Volume of water in ³₅ of the bucket = 24300 cm³ 

Volume of the bucket
= 24300 ÷ ³₅
= 24300 x ⁵₃ 
= 40500 cm³ 

(b)
Volume of the container
= 90 x 45 x 50
= 202500 cm³ 

Number of buckets to fill the container
= 202500 ÷ 40500
= 5 r 0

Minimum number of buckets to fill the container
= 5 + 1
= 6

Answer(s): (a) 40500 cm³; (b) 6